Simulating Gygax's Stupid Economy

Some notes before I just copy and paste this whole thing:

  • I'm using a pound/shilling/penny coin denomination, with a ratio of 1L : 20s : 240d.
  • I opt for 2 mile hexes because I think that's fun.
  • I assume a very simple calendar with 12 months of 4 weeks each.

There's no good reason for this post; it's 3 AM and I was bored after finals, so I treated myself to one big stupid math problem. Is there a reasonable way to simulate a fantasy economy sorta transitioning from feudalism to capitalism? No, not really.

At best, you can use this to make sorta informed economic decisions about the game-world. Run into a hex? Roll 1-6 to see how many villages of people are on there. Want to make them pay you taxes? You get 2L from every village. Want to hire people? It costs 1L to hire 1 person for a year. Want to know how productive agriculture should be to be viable as an industry?

(I hope) I got you.

Agriculture & Population

A good farmer does not put all their eggs in one basket by sowing all their land at once. Consider a property of thirty acres. Ten acres would be sown and later harvested; another ten would serve as pastures for livestock; the ten left would be left to fallow. Suppose then a ratio that for each bushel of wheat sown on an acre, the ground yields 3 bushels; ten acres would yield 30 bushels. Further supposing that 1 bushel feeds one person for a month, or that 12 bushels feed one person for a year [1], those ten acres would feed two and a half people for a year.

The primary unit of land with which we are concerned is the hide, usually treated as 120 acres. Out of these 120 acres, only 40 are sown, though this yields still 120 bushels of wheat, which is enough to feed ten people. The institution of the tithe ensures that one tenth of output is given to the Church. That is not all: we can suppose that the value of the output is 1L, i.e. 2d per bushel, since indeed the hide is more accurately treated as a plot of land that produces 1L in value rather than a plot of 120 acres in particular. The feudal state extracts 2s, i.e. ⅒L, from the total output. In short, whether in bushels or in shillings, the Church and the state are each entitled a share equal to one tenth of the hide’s produce. The 96 bushels leftover is enough to feed eight people, and so for a conservative estimate of four people per household, we can assume that for every individual farmer there is one non-farmer.

This conservative estimate facilitates the simulation of populations with medieval technology, albeit not necessarily with medieval social relations. Hides were often measured in sets of five so that every five hides could provide one fully armed soldier in times of war. Five hides support up to one forty individuals in total, and so for every forty persons there is one fully armed soldier. Then each hide is expected to provide one individual for garrison duty; if we include the fully armed soldier among their numbers, then we expect in total one soldier for every eight people. One unit of 20 soldiers requires 160 people from twenty hides [2]. Five units of 100 soldiers, including one unit of 20 fully armed soldiers, requires 800 people from one hundred hides [3]. Thus the mass scale works well for national conflicts, whereas conflicts between smaller fiefs is better expressed using the one-on-one scale. From now on I shall refer to five hides as a quintet.

Suppose that there are from 40-240 people on any territory represented as a wargaming hex that is 2 miles across. Half of these are farmers, and again we suppose that there are four farmers to a hide. For every 40 people, there is a quintet supplying them and five troops (one fully armored). Since there are at most 2210 acres in such a hex, we cannot expect there to be more than maybe fifteen hides in one territory. In the case of such an urban center, simply refer to the 1:1 ratio of farmers to non-farmers, and allow there to be adjacent hexes with the necessary number of hides. For example, an urban center with 240 people requires 240 farmers on 12 quintets (i.e. 60 hides) on adjacent hexes. These adjacent rural hexes cannot have any urban features since all surplus output is redirected to the external urbs.

One acre costs 4d [4], so we can price land at about 10L per quintet or 35L per hex. One ox costs 30d; hence it costs about 1,200d or 5L for enough oxen to equip a quintet, which divides evenly into 1L per hide.

Industrial Development in the City

Urban denizens make an income equal to that of a peasant, 240d (i.e. 1L) a year [5]. As with the peasant, one tenth of this income is tithed and another tenth is taxed. Since a bushel of wheat costs 2d, a year of especially plain food costs 24d (another tenth). It costs 60d to rent a cottage in the city, and this constitutes a quarter of a laborer’s total income.

One important thing is that in this situation, laborers and peasants pay the same amount of taxes. You can thus expect a single quintet to generate 960d or 4L in revenue, i.e. a settlement will generate 1L in taxes for every ten individuals. Also important to note is that since taxes are levied in terms of money rather than in crop yield, as per the usual rules for strongholds, we anticipate an economy where things are produced for exchange such that economic and political power is expressed through an accumulation of commodities. That is to say that the economy at large is capitalist as opposed to feudal per se.

It would be wise to own any industrial operations on the premises, since your taxes would then represent a return on whatever you invested in wages each week. Because each worker costs 5d a week, suppose you were to hire 20 at a time – this is an industrial operation, after all. You would spend 100d a week on your workers’ time, something like 12 hours a day for 6 days a week, but we need only worry about weeks. Provided you are keeping up with demand for the product, and your workers are producing at a rate comparable to society at large, the product will be worth more than it cost in labor and ingredients. This is because the social value necessary to reproduce labor power for a time, i.e. by paying your workers their wages so they can buy food et cetera to live, is less than the social value embedded in the workers’ product. The extent to which the product is more socially valuable than the labor time invested in it is expressed as a proportion of surplus value generated per quantity of wages, or the rate of exploitation.

Edit: The Surplus/Year column would be correct for five employees, but not for twenty. Therefore multiply the values in that column by four. The subsequent table for annual value in pounds is correct.

This does not account for social value embedded in the product due to things such as machinery or materials. Such factors, however, do not increase the rate of exploitation because they do not contribute new value to the product, as much as they transfer social value from one previous product to a new one. Labor accomplishes this transmutation and, again, the social value necessary to reproduce labor time is less than the social value generated in that time. Moreover, sellers of products will not be eager to sell things for less than they can be exchanged given the social value embedded in them. Therefore you may simply add such constant costs to the overall value of the product while knowing that you spend that same amount anyway. Without taking costs like that into account, it will cost 20L to employ 20 workers a year, which is the most you can pull from a mixed population of 100 (double that for an urban population).

Industrial Development in the Country

At this point in time, the productivity of agriculture is too low to become a proper industry. Even in the real world, the agricultural and dairy industries are heavily subsidized because they are unreliable. There is a reason that peasants are at the root of the operation: by owning their own labor time and whatever necessary materials, the cost of time is basically minimized and not paid as wages. They are able to feed themselves with what they grow, and sell whatever remains. It would be a mistake to invest in agricultural enterprises while they are so inefficient in terms of how much surplus value you extract from time invested.

To make a fair comparison, let us suppose that peasants produce only for exchange and thus sell all their produce. Four peasants can cooperate and generate 240d in revenue. Minus tithes and rent, they have 192d leftover; meanwhile, they also get to live on the land which they work, so they need to only purchase 4 * 24d = 96d in food. This leaves 96d leftover. On the other hand, it would cost 4L to employ laborers to work that land, and so they would have to be four times as productive to attain the same revenue as their peasant counterparts. This is a money-burning strategy.

Let us suppose that the land itself becomes four times as productive such that only one person need tend to the soil that used to require four people. This results in there being a quarter of the farmers there used to be, so that the price of wheat remains at 2d per bushel or 24d for a year’s worth of food. The one farmer produces still 240d in revenue on the land, but they accomplish this by themselves rather than in a group with three other farmers. This is still not a profitable venture because the minimum wage costs as much as one farmer generates, so there is a 0% rate of exploitation.

Then let us suppose the land increases in productivity, such that an individual farmer has gone from generating 0.25L to 1.00L to 1.25L over the years. To ensure the value of wheat itself remains intact, the number of farmers again decreases in proportion. Finally, you can invest 1L to employ a laborer to farm the same amount of land as before and generate a total value of 1.25L. That is a 25% rate of exploitation, made possible by increasing productivity and a proportional decrease in social effort dedicated to that product! This, of course, relies on the steady flow of peasants moving away from their ancestral fields rather than staying and trying to make bank; however, if they do not move away, eventually the value of wheat will be deemed lower since so much more is being produced by society as a whole in the same amount of time.

As the average productivity of the land improves, rather than fiddling with removing population from rural areas to cities, simply increase the population of cities in proportion to productivity. This then also accounts for an increasing population overall. The table below assumes that 20L are spent hiring 20 farmers a year.

The increase of population in urban centers corresponds with a proportional increase in available workforce for factories and militaries. To keep things from getting too finicky, while also allowing for the possibility to invest in agricultural industry, you might restrict the technological advancement of the game-world to a ratio of 1 farmer for every 5 non-farmers. Then at this point, you could treat the hiring of workers by hundreds instead of twenties (given the urban multiplier of 5). This will make translating rates of exploitations into money generated much more easily (20% --> 20L), and allow you to deal with 100L for hiring 100 workers which is a nice, round number. Even more convenient is that since there are 5 farmers for every 20 non-farmers, the population of any individual hex can be expressed as being from 100-600 instead of 40-240; or a wholly rural hex of 40 farmers can support a separate urban hex of 200 non-farmers. You do the math.

[1] I had read that a gallon loaf, a load of bread made using a gallon of wheat (i.e. one eighth a bushel), was considered to be the weekly ration of the poor. However, since each loaf is about 8.7 lb, that means that for someone to eat one load a week results in only ~1,500 calories a day. It would make sense to just double what is eaten, then. This increases the bushels consumed per year from 6 (for 48 gallon loafs, one a week) to 12 (for 96 gallon loafs, two a week).

[2] The 1:20 scale for mass combat is common in wargames, including Chainmail and the original 1974 edition of Dungeons & Dragons.

[3] In fact, a shire might be considered to have 100 hides or 20 fives of hides (‘quintets’). Never mind!

[4] One teamland or virgate, which is one fourth a hide and thus 30 acres, costs 10s or 120d. Therefore an acre costs 4d, and you could purchase a single hide for 2L.

[5] My source technically lists the cost of a laborer as being 2L a year, but then it says that maidservants and manservants cost only 1L a year. I assume that by laborer, it means specifically someone doing hard labor. Therefore, while simulating the rise of early industry, I think it’s appropriate to price labor at just 1L, especially because from what I understand, early workers were often young unmarried women.

Ask me for sources.


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